Exact Solutions of a Power Law Fluid Model in Posttreatment Analysis of Wire Coating with Linearly Varying Boundary Temperature

Rehan Ali Shah, Saeed Islam, Abdul Majeed Siddiqui, Tahira Haroon

Department of Basic Sciences and Islamiat, University of Engineering and Technology, Peshawar, Pakistan.
Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan.
Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan.
Department of Mathematics, Pennsylvania State University, York Campus, York, USA.

DOI: 10.4236/am.2013.42050                

Abstract

In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.

Keywords

Exact Solution; Wire Coating; Power Law Fluid Model; Linearly Varying Temperature at Boundaries

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. M. Denn, “Process Fluid Mechanics,” Prentice-Hall, Upper Saddle River, 1980.
[2]	S. Middleman, “Fundamentals of Polymer Processing,” McGraw-Hill, New York, 1977.
[3]	J. M. McKelvey, “Polymer Processing,” John Wiley and Sons, New York, 1962.
[4]	J. B. Paton, P. H. Squire, W. H. Darnell, F. M. Cash and J. F. Carley, “Processing of Thermoplastic Materials,” Reinhold Pub. Corp., New York, 1959, pp. 269-299.
[5]	E. B. Bagley and S. H. Storey, Wire and Wire Products, Vol. 38, No. 7, 1963, pp. 1104-1122.
[6]	S. Akter and M. S. J. Hashmi, “Analysis of Polymer Flow in a Canonical Coating Unit: Power Law Approach,” Progress in Organic Coatings, Vol. 37, No. 1-2, 1999, pp. 15-22. doi:10.1016/S0300-9440(99)00045-4
[7]	S. Akter and M. S. J. Hashmi, “Plasto-Hydrodynamic Pressure Distribution in a Tepered Geometry Wire Coating Unit,” Proceedings of the 14th Conference of the Irish Manufacturing Committee Dublin, Vol. 37, No. 3, 1997, pp. 331-340.
[8]	A. M. Siddiqui, T. Haroon and H. Khan, “Wire Coating Extrusion in a Pressure-Type Die in Flow of a Third Grade Fluid,” International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10. No. 2, 2009, pp. 247-257.
[9]	R. T. Fenner and J. G. Williams, “Rheological Analysis of Stabilizing Forces in Wire Coating Analysis,” Trans. Plastic Inst. London, Vol. 35, 1967, pp. 701-706.
[10]	M. Sajjid, A. M. Siddiqui and T. Hayat, “Wire Coating Analysis Using MHD Oldroyd 8-Constant Fluid,” International Journal of Engineering Science, Vol. 45, No. 2-8, 2007, pp. 381-392.
[11]	M. Kasajima and K. Ito, “Posttreatment of Polymer Extrudate in Wire Coating,” Applied Polymer Symposium, No. 20, 1973, pp. 221-235.
[12]	H. I. Andersson and F. Irgens, “Film Flow of Power-Law Fluids,” Encyclopedia of Fluid Mechanics, Polymer Flow Engineering, Vol. 9, 1990.